Abstract : Formulations of the equivalence theorem only involving electric currents either imply non-null inner fields, or the inclusion of a bulk perfect magnetic conductor. The possibility of maintaining a homogeneous background medium across the equivalent-current surface and null inner fields without recurring to magnetic currents is here investigated for the case of cylindrical sources. The proposed procedure keeps using the definition of equivalent electric currents as found in A. Love's theorem, introducing further layers of auxiliary electric currents to mimic the role of the missing magnetic ones. Optimal scalar coefficients applied as weights on each layer current are found, so to minimize the mean quadratic error in the fields radiated outside the auxiliary shell region, while at the same time minimizing internal radiation. The procedure is inherently well-conditioned, thanks to the reduction in the number of degrees of freedom involved, equal to the number of layers, as forced by a regression approach. A thorough numerical analysis is presented, where residual errors are found to be in the range of a few percent points.